Spray furniture cleaner over the surface of the piece, then wipe with a dusting rag. Repeat as necessary on any stubborn, sticky spots, and thoroughly clean the entire piece to remove any dirt, grease or debris. While you're dusting and cleaning, make note of any scratches or discolorations on the piece.
Dab a small amount of the black shoe polish onto a clean rag. On an inconspicuous area of the furniture, such as the underside or inside a drawer, rub in a small amount of the shoe polish to test how well the shoe polish will work on this piece. If you do not like the outcome of the test, do not proceed with polishing the rest of the piece.
Dab more shoe polish onto the rag and wipe it onto scratches and discolorations. Let the shoe polish sit for a few minutes so the colorant can penetrate the wood and permanently stain the scratches. Use the second clean cloth to wipe up any excess and gently buff the scratched areas.
Wipe shoe polish across the entire piece, working the rag in sweeping, circular motions. Allow the shoe polish to dry.
Buff the entire piece of furniture with the second clean cloth, until the furniture has a nice luster.